Transient effects in the backscattered current of a Luttinger liquid

TL;DR

This paper investigates how a transient impurity affects the backscattered current in a Luttinger liquid at finite temperature, revealing how switching dynamics influence transport properties and proposing a method to measure the interaction parameter.

Contribution

It introduces a dimensionless parameter to characterize impurity switching relevance and suggests a new experimental approach to determine the Luttinger parameter K.

Findings

The impurity switching process significantly distorts static impurity results.

A dimensionless parameter τ_R determines the relevance of switching effects.

Time measurements can potentially reveal the Luttinger parameter K.

Abstract

We study the backscattered current in a Luttinger liquid in the presence of a point like weak impurity switched on at finite time, taking into account finite-temperature effects. We show how the well-known results for a static impurity are distorted. We derive a dimensionless parameter $\tau_{R}$ as function of the electron-electron interaction and the temperature, such that for $\tau_{R} < 1$ ($> 1$) the switching process is relevant (irrelevant). Our results suggest the possibility of determining the value of the Luttinger parameter $K$ through time measurements in transport experiments at fixed voltage.